You might contact the GHIN folks who have the data on 2.3M golfers for this information… Or maybe ask the folks at ARCCOS golf as they have been tracking data for a while, not sure for how long.
Several years ago, I wrote to the group that handles Shotlink and asked about some putting stats… and they were kind enough to share the data… which previously had never been published. My point, is sometimes asking can get you what you want.
Now as to your specific question… how many years in a row would a person have to have an 18 HCP for you to be satisfied? Then over how long a period could they take to become a 5? One year, two years, … I am asking since the details would have to be very specific to query the database.
Hope you find out and can share it.